Finite Group Databasebeta

← Group #13014495

Character table — Group #13014495

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size112444445588810161616161616162020202020202020202020323232323240408080808080808080
order12244451022241028820202020204448888888810404040402444444488
χ111111111111111111111111111111111111111111111111
χ2111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-111
χ311111111111111-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1
χ411111111111111-1-111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-11111-1-1
χ51111111111-1-111i−i111-1-111111111111-1ii−i−i-1-1-1-1ii−i−ii−i
χ61111111111-1-111i−i111-1-1111-1-1-1-1-1-1-1-1-1ii−i−i-1-111−i−iiii−i
χ71111111111-1-111−ii111-1-111111111111-1−i−iii-1-1-1-1−i−iii−ii
χ81111111111-1-111−ii111-1-1111-1-1-1-1-1-1-1-1-1−i−iii-1-111ii−i−i−ii
χ911111111-1-1111-11111111-1-1-1iiii−i−i−i−i11111-1-1i−ii−ii−i-1-1
χ1011111111-1-1111-11111111-1-1-1−i−i−i−iiiii11111-1-1−ii−ii−ii-1-1
χ1111111111-1-1111-1-1-111111-1-1-1iiii−i−i−i−i1-1-1-1-1-1-1i−i−ii−ii11
χ1211111111-1-1111-1-1-111111-1-1-1−i−i−i−iiiii1-1-1-1-1-1-1−iii−ii−i11
χ1311111111-1-1-1-11-1i−i111-1-1-1-1-1iiii−i−i−i−i-1ii−i−i11−ii-111-1−ii
χ1411111111-1-1-1-11-1i−i111-1-1-1-1-1−i−i−i−iiiii-1ii−i−i11i−i1-1-11−ii
χ1511111111-1-1-1-11-1−ii111-1-1-1-1-1iiii−i−i−i−i-1−i−iii11−ii1-1-11i−i
χ1611111111-1-1-1-11-1−ii111-1-1-1-1-1−i−i−i−iiiii-1−i−iii11i−i-111-1i−i
χ172222-2-222222-222002-2-2-2-2-2-2200000000200002-200000000
χ182222-2-22222-2222002-2-222-2-2200000000-20000-2200000000
χ192222-2-222-2-22-22-2002-2-2-2-222-20000000020000-2200000000
χ202222-2-222-2-2-222-2002-2-22222-200000000-200002-200000000
χ21444444-1-10044-1044-1-1-1-1-100000000000-1-1-1-1-10000000000
χ22444444-1-10044-10-4-4-1-1-1-1-100000000000-111110000000000
χ23444444-1-100-4-4-104i−4i-1-1-111000000000001−i−iii0000000000
χ24444444-1-100-4-4-10−4i4i-1-1-111000000000001ii−i−i0000000000
χ254444-4-4-1-1004-4-1000-1111100000000000-1i5−i5i5−i50000000000
χ264444-4-4-1-1004-4-1000-1111100000000000-1−i5i5−i5i50000000000
χ274444-4-4-1-100-44-1000-111-1-10000000000015−5−550000000000
χ284444-4-4-1-100-44-1000-111-1-1000000000001−555−50000000000
χ29444-4004444004400-4000000-400000000000000000000000
χ30444-40044-4-4004-400-4000000400000000000000000000000
χ3144-4000444400-4-400000000002i2i−2i−2i2i2i−2i−2i000000000000000
χ3244-4000444400-4-40000000000−2i−2i2i2i−2i−2i2i2i000000000000000
χ3344-400044-4-400-44000000000022-2-2-2-222000000000000000
χ3444-400044-4-400-440000000000-2-22222-2-2000000000000000
χ354-4002i−2i4-44-400000002i−2i002i−2i0−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000
χ364-4002i−2i4-44-400000002i−2i002i−2i02ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000
χ374-4002i−2i4-4-4400000002i−2i00−2i2i0−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000
χ384-4002i−2i4-4-4400000002i−2i00−2i2i02ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000
χ394-400−2i2i4-44-40000000−2i2i00−2i2i0−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000
χ404-400−2i2i4-44-40000000−2i2i00−2i2i02ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000
χ414-400−2i2i4-4-440000000−2i2i002i−2i0−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000
χ424-400−2i2i4-4-440000000−2i2i002i−2i02ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000
χ43888-800-2-20000-200020025−2500000000000000000000000000
χ44888-800-2-20000-2000200−252500000000000000000000000000
χ451616-16000-4-4000040000000000000000000000000000000000
χ4616-16008i−8i-44000000000−2i2i0000000000000000000000000000
χ4716-1600−8i8i-440000000002i−2i0000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.